In tomography, measurements are taken though multiple views of a subject (e.g., human or animal in biomedical applications), and mathematical algorithms are used to convert these measurements into three-dimensional (3-D) images of the subject. Such algorithms are referred to as tomography image reconstruction algorithms.
Example tomography image reconstruction algorithms can be performed by successive approximation methods, such as iterative maximum likelihood (ML) expectation-maximization algorithms. In an iterative ML algorithm, an image is updated using a gradient-based function at each iteration. The gradient function is calculated using a forward projection function, which describes how the 3-D image maps to the data space.
However, this forward projection is mathematically ill-posed. For example, noise in the measurements is amplified by the image reconstruction algorithm, degrading the image quality. Filtering can reduce the noise, but at the expense of image resolution and contrast.
An example imaging technique is positron emission tomography (PET). Generally, in PET and similar imaging methods, radioactive isotopes are injected into a subject. Decay of the isotopes (that is, a positron-electron annihilation event) results in photons being emitted from inside the animal. In conventional PET, detectors positioned outside the animal detect emitted photon pairs when they hit the detectors. These interactions are recorded, including the detection location and the energy. Based on these recorded interactions, an image of where the radioactive isotope is distributed in the body can be imaged using a tomography image reconstruction algorithm. PET is a widely used clinical imaging procedure for applications such as, but not limited to, staging and monitoring disease in cancer patients.
Conventionally, emitted photons from a source that are detected in coincidence by the detectors are used to reconstruct the 3-D tomographic images. So-called true coincidence events are assumed to have occurred somewhere along the line between two photons detected within a preset coincidence time window. Thus, a line can be determined between the photon pair based on the location of the detected photons, and the determined lines can be used to construct the image.
However, a large majority of the events detected by the detectors are not true coincidence events, but rather single photon events. It has been estimated that single-photon events make up about 90% of all detected events in a human PET system. Conventional PET systems do not use these single photon events to produce images. Alternate detector designs can be used to produce images from single photons. However, single photons do not provide images of the same resolution as that of coincidence photons, even though there are more single photon events. Thus, conventional PET systems ignore single photon events, and large amounts of available information remain unused, reducing the signal-to-noise ratio of the reconstructed image.